The present invention relates to discrete-time analog filters, also called sampled-data filters. The invention particularly relates to those filters intended for use with signals having frequencies or sampling rates in the range of several hundred megahertz to a few gigahertz.
A sampled-data filter may be formed of charge-transfer devices, such as charge-coupled devices. One such filter is a bandpass filter. For many applications, the sampling frequency for the signal input to such a filter may be very high, on the order of several hundred megahertz to a few gigahertz. A typical bandpass filter must meet specifications for a number of performance criteria, including passband width, transition width, and stopband rejection. If the filter is an "agile" bandpass filter for which the filter characteristics are changeable, additional performance criteria such as the speed with which changes are effected are also specified. Typically, changes in filter characteristics must be accomplished quickly, within a few cycles of the sampling frequency.
Discrete-time filters have typically been implemented using conventional analog finite-impulse-response (FIR) filters having analog coefficient multipliers, as shown in FIG. 1. A conventional analog FIR filter has an input delay line 10 with a plurality of taps 12, each having a tap weight. Each tap weight is an analog value to be multiplied by the signal tapped from the input delay line. The outputs of the taps 12 are combined in a summer 14 to form the output from the filter. Experience has shown, however, that the tolerance of each analog tap-weight value is difficult to control. Thus, the filter may not be accurately repeatable or reproducible. Further, when the sampling frequency is high, on the order of several hundred megahertz to a few gigahertz, it has been found that it is difficult to multiply the incoming high-frequency signal by these analog-coefficient multipliers and obtain accurate results because of the difficulties of high-speed multiplication. In addition, for an "agile filter", it is difficult to change the analog coefficients of the tap weights quickly, and maintain sufficient accuracy in those coefficients and the multiplication process.
In an attempt to improve somewhat on the performance of the conventional analog finite-impulse-response filter, the use of digital tap weights in association with each tap has been suggested. One accurate method to digitally implement the tap weights is by multiplying digital-to-analog converters; however, this method is restricted to low sampling-rate frequencies.
A structure for digitally implementing the tap weights for higher-speed operation is shown in FIG. 2. In such a finite-impulse-response filter, several binary-analog correlators (BAC's) 20 are connected in parallel. Each BAC 20 is a separate finite-impulse-response filter in which the coefficient multipliers in each tap 22 are the corresponding bits of the several filter coefficients when expressed as binary numbers. Each bit of each filter coefficient is mechanized using one BAC 20. As many BAC's are used as there are bits in each binary filter coefficient. The first BAC filter 20a uses for its tap weights or coefficient multipliers only the most-significant bit of each coefficient. The second filter 20b uses for its tap weights only the second-most-significant bit of each coefficient, and so on. As many of these binary-analog correlators are connected in parallel as there are bits in the multiplier coefficients. The output of each correlator is weighted appropriately in a weighting element 24 to correspond to the significance of the bit of that correlator in the coefficient multipliers. The weighted outputs are then summed in an output summer 26 to obtain the desired filter output.
Each tap multiplier 22 in the BAC filter therefore has a binary-coefficient, resulting in a known accuracy of multiplication for high-frequency signals; but, since the filter requires as many separate binary-analog correlators 20 as there are bits specified in the coefficient multipliers of the filter, these filters generally occupy too much circuit space, consume too much power, are too expensive for most practical systems. In addition, the large number of individual binary-coefficient multipliers, each with its own reliability and tolerance characteristics, may reduce overall system reliability.
In addition, each of the numerous delay elements in each BAC forming the filter has its own charge-transfer inefficiency, further contributing to the performance error for the overall filter. For example, a sampled-data filter may be designed for operation at a sample frequency of 870 MHz, with a 3 MHz passband width, a 95 DB stopband rejection, a transition frequency of 6 MHz, and intended to change frequencies in 6.7 nanoseconds. If each tap weight is approximated as a fourteen-bit binary number, with one GaAs cell representing each bit, that filter may be implemented with a gallium arsenide CCD-filter design with approximately 400 taps, if the charge-transfer-inefficiency variance is kept sufficiently small to keep the accuracy of the filter within acceptable limits. With N=400 taps, B=14 bits/tap, and 1 cell/bit, N times B=5600 cells are required to implement the filter. To keep the overall operation of the filter within any kind of acceptable limits, the variation in the charge-transfer inefficiencies of the cells must be kept to less than approximately 10.sup.-6. The yield of devices that meet such performance specifications is small, causing such filters to be prohibitively expensive.
For filtering signals having low sampling frequencies, such as speech, some work has been done on decimated or thinned analog and digital finite-impulse-response filters. These thinned filters have a greatly reduced number of weighting coefficients. An example of a thinned analog filter is shown in FIG. 3. This reduction in the number of filter coefficients is possible because FIR filter tap weights are generally, from an information-theoretic point of view, overspecified. Coefficient values may be removed from the filters, thereby making the corresponding points on the impulse-response curve zero. By interpolation, however, these missing points may be recovered with suitable accuracy. The filter formed by a thinned FIR filter with an interpolator coupled to the output may be viewed as a pair of filters, with the thinned filter connected in tandem with the interpolator. Papers discussing thinned FIR filters are:
1. M. W. Smith and D. C. Farden, "Thinning The Impulse Response of FIR Digital Filters", Proc. ICASSP 81; Mar. 30, 31, Apr 1, 1981; Atlanta, Ga., pp 240-242.
2. G. F. Boudreaux and T. W. Parks, "Thinning Digital Filters: A Piecewise-Exponential Approximation Approach", IEEE Trans., Vol. ASSSP-31, No. 1, Feb. 1983, pp. 105-113.
3. M. V. Thomas, Y. Neuvo, and S. K. Mitra, "Two-Dimensional Interpolated FIR Filters", Proc. ISCAS 83, May 2-4, 1983; Newport Beach, CA, pp. 904-906.
4. Y. Neuvo, D. Cheng-yu, and S. K. Mitra; "Interpolated Finite Impulse Response Filters", IEEE Trans. Acoustics, Speech, and Signal Processing, Vol. ASSP-32, No. 3; June 1984, pp. 563-570.
Different studies have suggested that, in most instances, one may omit from a finite-impulse-response filter having multiple coefficient multipliers one out of two coefficients, three out of four coefficients, or seven out of eight coefficients. Interpolation of the filter output restores the signal. Nevertheless, the same number of delay elements on the input delay line for the filter is necessary so the tap coefficients that remain in the filter properly operate on the input signal and combine in the summer at the proper time.
Each tap weight or coefficient multiplier 32 of the thinned filter is an analog value, as in the conventional analog FIR filter. Such analog multipliers are acceptable for low-frequency signals, such as voice, but are inappropriate for high-frequency signals in the gigahertz range because of the difficulty in accurate multiplication, as discussed above. Thus, these decimated or thinned filters have been used in telephone and other low-frequency systems; but, the problems of multiplying the input signals by the analog coefficients accurately enough and fast enough for high-frequency sampled-data signals such as are used in high-frequency communication systems have prevented their use there. In addition, the problems associated with rapid changes of the filter coefficients in agile filters remain in the thinned or decimated filter.